This has been called a topsy-turvy season, yet even so, who knew Everton knew how to defend? At Goodison too, where more goals have been conceded by the home side than anywhere else in the Premier League.

Manchester City do not have the easiest attack to blunt, especially with Sergio Agüero back and looking close to peak sharpness, but Everton stood firm to take a slender advantage into the second leg of the Capital One Cup semi-final. That should ease some of the pressure on Roberto Martínez and some of the criticism of his players. Everton still have a lot to do at the Etihad, though here was evidence that Martínez’s talk of recovering from their lapses and learning from their mistakes may not have been the usual wishful thinking.

You could tell these were nervous times at Goodison by the way Everton players took it in turns to stress the importance of the crowd in this fixture. More than one mentioned the necessity of turning the place into a bear pit in order to make life as difficult as possible for City. And a little bit easier for the home players, ran the unsaid subtext. A crowd united in hostility towards opponents cannot find time for griping at its own side, which has been happening noticeably over the last few weeks.

This was Everton’s chance, a rare one these days, to give their supporters what Gordon Lee used to call a sniff of the Wembley hotdogs. Lee was the first manager to take Everton to the League Cup final, Martínez stands a chance of becoming the third. Perhaps more importantly he could still write himself into history as the first Everton winner, though he slightly missed striking the necessary can-do note by admitting beforehand that finishing in the top four would be more important than silverware this season. Managers of clubs who have seen precisely zero silverware in over 20 years should be careful of making statements like that, especially with the team languishing in the bottom half of the table.

Everton’s resistance was all the more impressive considering there were periods early in the first half when the contest looked uneven. One piece of control by Agüero in the first few minutes was a statement of intent on its own, and when David Silva and Yaya Touré joined in, finding each other easily with precisely weighted passes, one feared for the home side. Yet, though initially out-thought, as they had been against Tottenham on Sunday, Everton refused to be overawed and refused to buckle.

Martínez had indicated he wanted to see an end to the soft goals being conceded at home and there was nothing close to a goal for the visitors in the opening 45 minutes. For all City’s purposeful start they never succeeded in finding a way through their opponents, Joel Robles did not have a save of note to make before the interval. Willy Caballero was twice beaten by John Stones and Romelu Lukaku from offside positions before Ramiro Funes Mori just managed to beat the flag to snaffle a legitimate opener in stoppage time.

What summed up Everton’s dogged resistance best was the sight of Muhamed Besic dispossessing Touré in full flow midway through the first half. Initially caught out by the Ivorian’s powerful surge, Besic refused to give up and stuck to Touré like a terrier snapping at the taller man’s heels. Just as the City player reached the edge of the area and shaped to part with the ball Besic whipped it from his toes and departed downfield with it, leaving Touré in a crumpled heap appealing for a free-kick that was never going to be given.

Besic does not quite fit the School of Science template, but he is a thoroughly effective competitor. Agüero had a couple of half-chances snuffed out by Stones and Funes Mori before Everton took the lead, but the goal at the end of the first half was by no means out of the blue. Everton had held firm against City’s attacks, just as their manager had promised, and had been threatening Caballero’s goal before Ross Barkley produced a shot the goalkeeper could only parry.

Barkley could have put a gloss on the Everton performance right at the start of the second half when his teasing ball across goal was only inches away from allowing Lukaku a tap-in, a miss the pair may have cause to regret in Manchester in a fortnight, even if the striker did restore his side’s lead after Jesús Navas had brought City level.

It may be the case, a charge often levelled at Martínez teams, that Everton are still not quite clinical enough or ruthless in pressing home an advantage. Yet this was not a night for carping. Everton stood up for themselves, showed they can not only live with the best but come back against the best, and the home manager’s programme notes even contained a treasure for supporters who have begun to turn sceptical.

“Like Spurs, we have seen too many draws,” he said, before offering perhaps the ultimate Martínez soundbite. “But all of them have been closer to victories than defeats.” Agree with him or not, there goes your glass half-full man.

Football does not yet award any extra points for performances more deserving of a win than a draw, and even if it did, critics of Martínez might point out, it might then have to subtract a few for matches that were more like draws than victories, such as the one Everton won with the last action of the game at Newcastle United on Boxing Day, when Tom Cleverley’s header turned a scoreless stalemate into three points. This cup tie, to be fair, was not streaky or debatable. It was well won.And yes, Goodison was a bear pit. The atmosphere at the end was something to make all of Everton proud.